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A step by step analysis is given for the following questions,
1. Find an upper bound for the number of possible states in the game of chess, assuming that draw-by-repetition is enforced if the same position is repeated three times.
2. Find an upper bound for the number of possible moves in a single turn in the game of chess.
3. Use Question 2 above to find an upper bound for the number of possible sequences of moves in 10 consecutive turns in the game of chess.
4. Chess experts sometimes think 10 turns ahead, but do not consider every possible sequence of moves. Given a computer capable of processing one billion moves per second, find the maximum number of options it could consider at each move if it must think 10 turns ahead within a 3-minute time period. [Note: what we have called a "turn" is actually called a "half-move".]
write and graph a direct variation equation that passes through point
compare and contrast all techniques used to solve systems of linear equations substitution elimination and
A credit company allocates 8-digits accounts such as 1122-3421 where the digit 1 through 9 are used. How many different account numbers can there be?
How many arrangements are there if only any 4 teachers and no children are in the picture?
when we add subtract multiply and divide we discover there are basic properties that govern what we can and cannot do.
Prove that if M is a maximal ideal of S and phi is surjective then phi^-1(M) is maximal ideal of R. Give an example to show that this need not be the case if phi is not surjective.
Explain in your own words your understanding of the concept of slope as it relates to graphs of linear equations. Illustrate with examples. Also include in your explanation the use of slopes to determine parallel and perpendicular lines.
Make a graph for the quadratic function
How much of chemicals A and B remain after a long time?
Determine the width if the area of the field
a rational number plus an irrational number will be ____
Solve the following equation
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